The Riemann zeta function ζplays a crucial role in number theory as well as physics. Indeed, the distribution of primes is intimately connected to the non-trivial zeros of this function. We briefly summarize the essential properties of the Riemann zeta function and then present a quantum mechanical system which when measured appropriately yields ζ. We emphasize that for the representation in terms of a Dirichlet series interference [1] suffices to obtain ζ. However, in order to create ζ along the critical line where the non-trivial zeros are located we need two entangled quantum systems [2]. In this way entanglement may be considered the quantum analogue of the analytical continuation of complex analysis.

In recent years sum frequency conversion processes have become an established tool to implement quantum information transfer interfaces between systems of different wavelengths. Such interfaces are essential for the realization of quantum networks, which combine different individual components with incompatible frequencies. In particular, long distance quantum communication, which uses stationary qubits with transitions in the visible or UV and flying qubits at telecommunication wavelengths rely on practical quantum frequency converters. Here, we present our work on the realization of sum frequency generation processes from telecommunication regime to visible and UV wavelengths and discuss cw and pulsed light characteristics

I will report on recent results obtained with cold atoms in fibre microcavities at Imperial College London and at the Laboratoire Kastler-Brossel in Paris. In the London experiment, we show how the Hamiltonian eigenstates of the system can be revealed through spectroscopic measurements despite the fast decoherence rate of the microcavity. We observe an avoided crossing in the dressed cavity spectrum, usually taken as evidence of strong coupling, notwithstanding the complete overdamping of Rabi oscillations in our experiment. We interpret this as dipole-induced transparency of the cavity, relying on destructive quantum interference to uncover the normal modes which might be expected to lie obscured [1]. In the Paris experiment instead, the atom-cavity coupling rate greatly exceeds every loss rate allowing to reach the single-atom strong coupling regime and to perform almost non-destructive measurements. Building on this we have developed a method based on the quantum Zeno dynamics to create symmetric entangled states in ensembles of several tens of atoms. We characterize the resulting states by performing quantum tomography, yielding a time-resolved account of the entanglement generation. In addition, we study the dependence of quantum states on measurement strength and quantify the depth of entanglement. Our results show that quantum Zeno dynamics can be used as a versatile tool for fast and deterministic entanglement generation [2].
[1] Y.-H. Lien, G. Barontini, M. Scheucher, J. Goldwin, and E. A. Hinds, in preparation
[2] G. Barontini, L. Hohmann, F. Haas, J. Estéve, and J. Reichel, Science 349, 1317 (2015)

I will report on recent results obtained with cold atoms in fibre microcavities at Imperial College London and at the Laboratoire Kastler-Brossel in Paris. In the London experiment, we show how the Hamiltonian eigenstates of the system can be revealed through spectroscopic measurements despite the fast decoherence rate of the microcavity. We observe an avoided crossing in the dressed cavity spectrum, usually taken as evidence of strong coupling, notwithstanding the complete overdamping of Rabi oscillations in our experiment. We interpret this as dipole-induced transparency of the cavity, relying on destructive quantum interference to uncover the normal modes which might be expected to lie obscured [1]. In the Paris experiment instead, the atom-cavity coupling rate greatly exceeds every loss rate allowing to reach the single-atom strong coupling regime and to perform almost non-destructive measurements. Building on this we have developed a method based on the quantum Zeno dynamics to create symmetric entangled states in ensembles of several tens of atoms. We characterize the resulting states by performing quantum tomography, yielding a time-resolved account of the entanglement generation. In addition, we study the dependence of quantum states on measurement strength and quantify the depth of entanglement. Our results show that quantum Zeno dynamics can be used as a versatile tool for fast and deterministic entanglement generation [2].
[1] Y.-H. Lien, G. Barontini, M. Scheucher, J. Goldwin, and E. A. Hinds, in preparation
[2] G. Barontini, L. Hohmann, F. Haas, J. Estéve, and J. Reichel, Science 349, 1317 (2015)

Atom interferometry constitutes nowadays one of the most promising and realistic forefronts in the accomplishment of quantum-based technologies. Parallel to the evolution of free-falling atom interferometers, new concepts with trapped and guided atoms have been developed in the last few years. Due to the large control over the atomic wavefunction and to the long interrogation times, an outstanding combination of high sensitivity and spatial resolution is expected to be achieved in compact and, ideally, portable devices. In this talk I will present our all-optical approach towards the realization of BEC-based guided interferometers. In particular I will discuss the recent results on the realization of a continuous Bragg splitter generated by the interference of two atomic waveguides. Progress towards the implementation on a miniaturized light chip will be finally reported.